In mildly alkaline medium, thiosulphate ion is oxidized by ${MnO}_4^{-}$ to " $A$ " the oxidation state of Sulphur in 'A' is

$8{MnO}_4^{-}+3{ S}_2{O}_3^{2-}+H_{2}O⟶8{MnO}_2+6{SO}_4^{2-}+2{OH}^{-}$

Let the oxidation state of Sulphur in $S{O}_4^{-2}$ is x

X+4(-2) = -2

X – 8 = -2

X= 6

Therefore, Oxidation state of Sulphur in “A” is 6.